GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 00:11

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In the xy-plane, triangular region S is bounded by the lines x=0,y=0,

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58364
In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

30 Nov 2016, 03:05
3
17
00:00

Difficulty:

35% (medium)

Question Stats:

76% (02:43) correct 24% (02:40) wrong based on 219 sessions

### HideShow timer Statistics

In the xy-plane, triangular region S is bounded by the lines x=0,y=0, and 3x−2y=30. Which of the following points does NOT lie inside region S?

A. (1,−1)
B. (2,−10)
C. (3,−13)
D. (5,−5)
E. (8,−2)

_________________
Manager
Joined: 02 Nov 2013
Posts: 72
Location: India
In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

30 Nov 2016, 04:01
1
1
This is how went with the problem,

Drawn the shaded region with using three lines x=0, y=0 and 3x-2y=30.

Went back to the answer choices and putting the x values verified the y values. All the points falling in the region should follow equation 3x-2y≤30.

Only answer choice with point (3,−13) does now follow this equation and the value of the equation comes as 35 which is beyond the shaded region.

Hope I am right ?
Attachments

Shaded region.png [ 10.76 KiB | Viewed 3545 times ]

Current Student
Joined: 07 Nov 2016
Posts: 8
Location: India
GMAT 1: 620 Q47 V29
GPA: 3.9
Re: In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

23 Feb 2017, 08:04
1
I just guessed the answer using the following method,

Using the equation 3x-2y=30, we can find x-intercept and y-intercept
if x=0, then y=-15
if y=0, then x=10
after plotting it on the plane , find the midpoint of these 2 points
(x1+x2/2, y1+y2/2)=(0+10/2,-15+0/2)=>(5,-7.5)

only one answer stands out (3,-13) -> D
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

24 Feb 2017, 06:24
1
Bunuel wrote:
In the xy-plane, triangular region S is bounded by the lines x=0,y=0, and 3x−2y=30. Which of the following points does NOT lie inside region S?

A. (1,−1)
B. (2,−10)
C. (3,−13)
D. (5,−5)
E. (8,−2)

For the point to lie in the specified region
1) Point should be in 4th quadrant (all options are of 4th uadrant)
2) Since 3x−2y=30 i.e. y = (3/2)x-15 so y must be greater than or equal to (3/2)x-15

Checking options
A. (1,−1) -1 > (3/2)(1)-15 Hence, Point lies in the region hence Incorrect Option
B. (2,−10) -10 > (3/2)(2)-15 Hence, Point lies in the region hence Incorrect Option
C. (3,−13) -13 < (3/2)(3)-15 Hence, Point does NOT lie in the region hence CORRECT Option
D. (5,−5) -5 > (3/2)(5)-15 Hence, Point lies in the region hence Incorrect Option
E. (8,−2) -2 > (3/2)(8)-15 Hence, Point lies in the region hence Incorrect Option

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director
Joined: 12 Nov 2016
Posts: 701
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

15 Jun 2017, 22:47
GMATinsight wrote:
Bunuel wrote:
In the xy-plane, triangular region S is bounded by the lines x=0,y=0, and 3x−2y=30. Which of the following points does NOT lie inside region S?

A. (1,−1)
B. (2,−10)
C. (3,−13)
D. (5,−5)
E. (8,−2)

For the point to lie in the specified region
1) Point should be in 4th quadrant (all options are of 4th uadrant)
2) Since 3x−2y=30 i.e. y = (3/2)x-15 so y must be greater than or equal to (3/2)x-15

Checking options
A. (1,−1) -1 > (3/2)(1)-15 Hence, Point lies in the region hence Incorrect Option
B. (2,−10) -10 > (3/2)(2)-15 Hence, Point lies in the region hence Incorrect Option
C. (3,−13) -13 < (3/2)(3)-15 Hence, Point does NOT lie in the region hence CORRECT Option
D. (5,−5) -5 > (3/2)(5)-15 Hence, Point lies in the region hence Incorrect Option
E. (8,−2) -2 > (3/2)(8)-15 Hence, Point lies in the region hence Incorrect Option

How do we know that the for the answer choices that y must be greater than the expression 3/2x - 15? How do we know that it must be y is greater than that then say y must be less than that value?
Director
Joined: 12 Nov 2016
Posts: 701
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

15 Jun 2017, 23:01
Bunuel wrote:
In the xy-plane, triangular region S is bounded by the lines x=0,y=0, and 3x−2y=30. Which of the following points does NOT lie inside region S?

A. (1,−1)
B. (2,−10)
C. (3,−13)
D. (5,−5)
E. (8,−2)

@Bunuel- although we can diagram this problem, calculate the x and y intercepts which would inevitably allow us to find the answer- can we not just reason that because we are given the hypotenuse of the triangle in this particular form 3x-2y=30 that no set of coordinates within the triangle will result in a number greater than 30? And when I say hypotenuse of the triangle I want to note I am not trying to make a generalization- there was another similar problem in ps made by manhattan in which the triangle in the plane had a x line and y line and an equation by the side it formed by connecting to the x and y lines turned out not to be the hypotenuse.
Intern
Joined: 20 Jun 2017
Posts: 7
Re: In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

03 Apr 2018, 07:24
Hi,
I do'nt understand why the point should satisfy the line eqn 3x-2y < = 30 and not required to satify x <= 0 and y <= 0 as both are the eqn of lines that make the triangle. I don'nt know the concept or logic applied . kindly help me with the basic concepts here Bunuel
TIA
Manager
Joined: 31 Dec 2018
Posts: 114
Location: India
Re: In the xy-plane, triangular region S is bounded by the lines x=0,y=0,  [#permalink]

### Show Tags

23 Apr 2019, 04:32
1
I have a different approach !

As per the graph mentioned by [#permalink] we are clear with x and y intercepts.
the equation of the line becomes:
y=(3/2)x -15

Slope of the line becomes 3/2 or 1.5
this means that when we move 1 unit in x we lose 1.5 units of y

Coming back to the question,
All options have valid x-axis values.
So, if we move 3 units in 3 we will lose 4.5 units of y intercept ie. y will be 15-4.5 = 10.5
But y-axis value is mentioned as -13, this shows that the point lies outside the region S.

Hope this helps !
Re: In the xy-plane, triangular region S is bounded by the lines x=0,y=0,   [#permalink] 23 Apr 2019, 04:32
Display posts from previous: Sort by